(x+6)(x-9)=54

Solution for (x+6)(x-9)=54 equation:

(x+6)(x-9)=54

We move all terms to the left:

(x+6)(x-9)-(54)=0

We multiply parentheses ..

(+x^2-9x+6x-54)-54=0

We get rid of parentheses

x^2-9x+6x-54-54=0

We add all the numbers together, and all the variables

x^2-3x-108=0

a = 1; b = -3; c = -108;
Δ = b2-4ac
Δ = -32-4·1·(-108)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-21}{2*1}=\frac{-18}{2}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+21}{2*1}=\frac{24}{2}
=12
$